A case for new data visualizations
5/25/23
History is filled with data visualizations, but some of the earliest references to 3D visualizations were in 1874 by James Clerk Maxwell.
Since then, studies have shown that 3D graphics are less effective at conveying information when a 2D equivalent is available. As of now, most of those studies focus on 2D projections of 3D graphics.
When to use 3D graphics
Relationship between multiple variables
Display data over 3D objects
When to NOT use 3D graphics
Does not add any additional information
Lack of interactivity
Research questions:
Our study draws influence from Cleveland and McGill’s 1984 paper, specifically from their position-length experiment with graph types 1 and 3.
Graph types for position-length experiment from Cleveland and McGill
In their study, participants were asked which of the marked bars were smaller and by approximately how much.
Values involved in comparison judgments are
\[V_i=10\cdot10^{(i-1)/12}\quad i=1,\dots, 10\]
To closely replicate values, we made two assumptions about the comparisons from Cleveland and McGill
Match the exact ratios that were used
No value was used more than twice
Treatment Design
There are 42 treatment combinations, too many for a busy subject!
Design of each kit
Each subject receives a bag of 3D printed kits with instructions that direct users to a Shiny app
Picture of kit here
\[y_{ijklm}=\mu+S_i+R_j+G(R)_{(k)j}+T_l+\epsilon_{ijklm}\]
where
\(y_{ijklm}=\log_2(|\text{Judged Percent} - \text{True Percent}|+1/8)\)
\(S_i\sim N(0,\sigma^2_S)\) is the effect of the \(i^{th}\) subject
\(R_j\) is the effect of the \(j^{th}\) ratio
\(G(R)_{(k)j}\) is the effect of the \(k^{th}\) graph type nested in the \(j^{th}\) ratio
\(T_l\) is the effect of the \(l^{th}\) comparison type
\(\epsilon_{ijklm}\sim N(0,\sigma^2_\epsilon)\) is the random error
| Term | SS | MS | Num DF | Den DF | F-value | P-value |
|---|---|---|---|---|---|---|
| ratio | 0.404 | 0.404 | 1 | 501.954 | 0.235 | 0.628 |
| type | 1.924 | 1.924 | 1 | 509.980 | 1.120 | 0.290 |
| ratio:plot | 0.447 | 0.224 | 2 | 498.247 | 0.130 | 0.878 |
In Cleveland and McGill, confidence intervals were calculated using bootstrap sampling of subjects using the means of the midmeans. The same process is used here, although each subject did not receive each treatment combination.
Some picture here
No results were significant, but what if we could incorporate the study at a larger scale?
Experiential learning with STAT 218 at University of Nebraska-Lincoln.